Two vectors $\overrightarrow{ A }$ and $\overrightarrow{ B }$ have equal magnitudes. If magnitude of $\overrightarrow{ A }+\overrightarrow{ B }$ is equal to two times the magnitude of $\overrightarrow{ A }-\overrightarrow{ B }$, then the angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$ will be .......................

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

The resultant of $\overrightarrow P $ and $\overrightarrow Q $ is perpendicular to $\overrightarrow P $. What is the angle between $\overrightarrow P $ and $\overrightarrow Q $

If $\vec{P}+\vec{Q}=\vec{P}-\vec{Q}$, then

What vector must be added to the two vectors $\hat i - 2\hat j + 2\hat k$ and $2\hat i + \hat j - \hat k,$ so that the resultant may be a unit vector along $X-$axis

A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)

${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$            ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$

${\vec F_3} =  - 6\hat i + 4\hat j - 7\hat k$         ${\vec F_4} =  - \hat i - 3\hat j - 2\hat k$

Then the particle will move